Can You Solve This 2D Equilibrium Problem with a Pirate on a Plank?

[Oblivion77]

Homework Statement

The pirate is walking the plank. If the plank weighs 500 N and the weight acts at
the centre of the plank, how far (distance x) can our pirate, who weighs 780 N, walk
before the plank tips and he falls. All dimensions are in meters. ANS: 0.769 m

(Look at picture)

Homework Equations

Sum of forces in X =0
Sum of forces in Y=0
Sum of moment(about a point) = 0

The Attempt at a Solution

I can get pretty far in the solving, but since there are 4 unknowns in the problem(and you can only solve for 3 unknowns in 2D I ran into a problem). The Pin support has 2 reactions and the other support is 1 normal force. Thanks for any help.

 

[PhanthomJay]

Hint: The Normal force (reaction) at the far left support must be 0 when the plank is about to tip (it is assumed that the left support is not anchored, such that it can take a downward load, but not an upward load.).

 

[Oblivion77]

Hint: The Normal force (reaction) at the far left support must be 0 when the plank is about to tip (it is assumed that the left support is not anchored, such that it can take a downward load, but not an upward load.).

Thank you so much! I got the answer :D